Table 3 places here, please.
Based on the frequentists approach showing non-significant regard to
HRV, rumination, and depression, which thereby failed to reject the null
hypothesis, Bayesian factor analyses (using JASP 0.16.3) were conducted
to assess the likelihood of a correct null hypothesis (Quintana &
Williams, 2018). Bayesian factor analysis is a development and
alternative to testing the null hypotheses significance test. The
Bayesian framework allows for the probabilistic description of
parameters and hypotheses and can quantify the degree to which the data
favors the null hypothesis (H0) or the alternative hypothesis (H1)
(Gelman et al., 2014; McElreath, 2020). The H1 is that HRV is negatively
correlated to rumination. The H0 rejects these correlations. In this
study, we use Bayes factor 10 (BF10) which measures the
degree to which H1 is supported by data compared with the H0. When the
BF is higher than 1, the evidence is in favor of H1. The larger the
factor, the higher the probability of the evidence in favor of H1. On
the contrary, when the BF is less than 1, the evidence is in favor of
H0. The smaller the factor, the higher the probability of the evidence
in favor of H0.
Bayesian analysis showed that there was strong evidence supporting no
correlations between HRV and RRStotal(BF10 = 0.152), Brooding (BF10 = 0.061),
and Reflection (BF10 = 0.41), because the
BF10 were less than 1.